Phil Foden opened the scoring before Haaland took centre stage with a second-half double as City bounced back from two consecutive Premier League defeats.
United went into a derby ahead of City in the Premier League table for the first time in five years.
But that owed more to City’s early season struggles than signs of progress for Amorim’s men, who have taken just four points from their opening four games and been dumped out of the League Cup by fourth-tier Grimsby.
City fans goaded Amorim with chants of “sacked in the morning” in the closing stages.
The Portuguese is not in danger of an immediate dismissal, but his Premier League record now reads a dismal eight wins in 31 games.
Liverpool remain top of the table after a late Mohamed Salah penalty gave them a hard fought 1-0 win at Burnley.
Arne Slot opted not to include record-signing Alexander Isak in his squad at Turf Moor, aiming to ease the former Newcastle forward in gently.
Liverpool almost paid the price for their lack of cutting edge until Hannibal Mejbri’s handball gave the champions a lifeline and Salah converted from the spot in the 95th minute.
Arsenal ensured Ange Postecoglou did not enjoy his return to north London in his first game as Nottingham Forest boss as the Gunners cruised to a 3-0 win on Saturday.
Martin Zubimendi was an unlikely hero, opening the scoring with a thunderous volley and heading in the third in between a goal from Viktor Gyokeres.
Tottenham sit behind Arsenal only on goal difference after a three-goal blitz of 10-man West Ham, thanks to goals from Pape Sarr, Lucas Bergvall and Micky Van de Ven after Tomas Soucek was sent off for the Hammers.
Chelsea missed the chance to go top after Fabio Carvalho’s goal in the 93rd minute salvaged a well-earned point for Brentford in a 2-2 draw, with substitute Cole Palmer and a blistering strike from Moises Caicedo on target for the Blues.
Nick Woltemade did his best to make Newcastle fans forget the departed Alexander Isak by scoring the only goal in a 1-0 win over Wolves on his debut while Bournemouth moved up to fourth after beating Brighton 2-1.
Leeds were undone by a 94th minute own goal by Gabriel Gudmundsson to lose 1-0 at Fulham while the matches between Crystal Palace and Sunderland and Everton against Aston Villa ended in goalless stalemates.